Functions with integer-valued divided differences

Abstract

Let $s_0,s_1,s_2,\dots$ be a sequence of rational numbers whose $m$th divided difference is integer-valued. We prove that $s_n$ is a polynomial function in $n$ if $s_n\ll {\theta }^n$ for some positive number $\theta$ satisfying $\theta <e^{1+\frac{1}{2}+\cdots +\frac{1}{m}}-1$.

18 pages; revised for clarity

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